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The structure of null Lagrangians. (English) Zbl 0662.49016
The familiar identification of null Lagrangians L(x,u,\(\nabla u)\) (for which the Euler equations are identities) with the divergences (i.e., \(L(x,u,u)=div P(x,u,\nabla u))\) is reformulated in the form \(L(x,u,\nabla u)=\sum L^ i(\nabla S^ i(x,u))\) (finite sum), where \(L^ i(\nabla v)\) are certain homogeneous null Lagrangians and \(S^ i(x,u)\) are appropriate functions. The result can be interpreted in terms of the multiple integral field theory.
Reviewer: J.Chrastina

MSC:
49Q99 Manifolds and measure-geometric topics
58A15 Exterior differential systems (Cartan theory)
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